Method of detecting signals in acoustic drill string telemetry

ABSTRACT

A method of acoustic telemetry in a drill string in a wellbore, comprises transmitting an acoustic signal related to a parameter of interest from a transmitting location into the drill string. The signals propagated through the drill string are detected at a receiving location, where the detected signals include noise. A drill string transfer matrix is determined defining the propagation of signals through a transfer interval between the receiving location and the transmitting location. The detected signals and the drill string transfer matrix are used for obtaining an estimate of the acoustic signal.

BACKGROUND OF THE INVENTION

[0001] 1. Field of the Invention

[0002] This invention is in the field of signal processing, and is morespecifically directed to acoustic drill string telemetry.

[0003] 2. Description of the Related Art

[0004] The petroleum industry relies heavily on the operation ofdrilling into the earth, both on land and offshore, in the explorationfor and production of petroleum products. Over the years, the morereadily found and accessible petroleum reservoirs have of course beendiscovered and depleted first. As a result, the exploration andproduction operations must necessarily concentrate to a greater degreeon less accessible and less readily discoverable reserves. In order toreach these locations, the depths of drilling have increased, thelocations at which drilling takes place have become increasinglydifficult and less accessible, and the drilling operations havenecessarily become more complex. Accordingly, drilling operations in thesearch for and production of petroleum products have become moreexpensive, with this trend likely to continue in the future. Because ofthis increasing cost, the accuracy and efficiency of the drillingoperation is becoming even more important.

[0005] The success and efficiency of the drilling operation depends to alarge degree on the quantity and quality of information that thedrilling operator has about the sub-surface structure into which thedrilling is taking place, and also about parameters concerning theoperation of the drill bit as it proceeds into the earth. Manytechniques for acquisition and communication of such information havebeen tried and used in the industry.

[0006] A system which utilizes the drill string as a medium for thetransmission of data is referred to as acoustic telemetry or stress wavetelemetry. Acoustic telemetry systems are known in the art. For exampleU.S. Pat. No. 5,477,505 to Drumheller and U.S. Pat. No. 5,303,203 toKingman describe such systems. The typical system includes transmitters,such as solenoids, eccentric motors, and piezoelectric transducers,which intentionally vibrate the drill string in a manner correspondingto the desired data. These data may include information concerningdrilling parameters and formation parameters. In the case of stress wavetelemetry the desired information is obscured by undesirable bit anddrilling noise that is also transmitted through the drill string.

[0007] It has been discovered that vibrations, whether from the drillbit itself or intentionally generated by transmitters, are notcommunicated through the drill string in an ideal manner, due to thenon-ideal response of the drill string to such vibrations. Conventionaldrill strings, which consist of a number of lengths of drill pipe joinedby pipe joints, inherently have frequency domain stopbands thatattenuate acoustical signals at the stopband frequencies. Thisfrequency-dependent attenuation can severely distort some signals. Otherfactors also distort the vibrations communicated along a drill stringfrom downhole to the surface. Such factors include noise generated bythe drilling fluid, or mud, which is conventionally pumped through thedrill string at relatively high pressures. This high pressure flow offluid causes significant vibrations in the drill string. Other devicesin the drilling operation, such as bearings in the swivels at the top ofthe drill string, the rattling of chains which turn the kelly bushing,or the motor in a top drive drilling arrangement, and the slap of thecasing against the drill string or well bore, also generate significantacoustical vibrations which are received by and transmitted along thedrill string. These vibrations are superimposed upon the desired datasignal, and will accordingly be detected at the top of the drill stringby such detectors as are attempting to detect the data signaltransmitted from the downhole location.

[0008] Considering the vibrations generated by a transmitter as “signal”and the vibrations generated by the drill bit and the other vibrationscaused by drilling mud flow and the mechanical sources discussed in theprior paragraph as “noise”, it has been found that the amplitude of thenoise can be substantially greater than the signal amplitude. Noise atthis level not only clouds the analysis of the information, but indeeddrowns out the information itself.

[0009] Vibration-state inference techniques have been described todetermine downhole force and displacement at a position close to the bitfrom similar measurements at a second location in the drillstring, (seeSPE 74718, Macpherson, et al., “Application and Analysis of SimultaneousNear Bit and Surface Dynamics Measurements”, SPE Drilling andCompletions, Society of Petroleum Engineers, December 2001). However,there is no suggestion therein of using such a technique for purposes ofacoustic telemetry in a drillstring.

[0010] The methods of the present invention overcome the foregoingdisadvantages of the prior art by providing a technique for removing aportion of the surface generated noise thereby improving the signal tonoise ratio of acoustic signals transmitted along a drill string.

SUMMARY OF THE INVENTION

[0011] In one aspect, a method of acoustic telemetry in a drill stringin a wellbore, comprises transmitting an acoustic signal related to aparameter of interest from a transmitting location into the drillstring. The signals propagated through the drill string are detected ata receiving location, where the detected signals include noise. A drillstring transfer matrix is determined defining the propagation of signalsthrough a transfer interval between the receiving location and thetransmitting location. The detected signals and the drill stringtransfer matrix are used for obtaining an estimate of the acousticsignal.

[0012] In another aspect, a method of reducing noise in an acousticsignal transmitted at a second location and received at a first locationin a drill string, comprises calculating a transfer matrix related to atransmission interval of the drill string. Time series data sets ofvibrations are detected at the first location comprising a firsttime-series data set of measurements related to a force on the drillstring and a second time-series data set of measurements related to anacceleration of the drill string. The first time-series data set and thesecond time-series data set are transformed to a frequency domain. Thetransformed first time-series data set and the transformed secondtime-series data set are combined with the transfer function to generatean inferred force related signal at the second location and an inferredacceleration related signal at the second location. The inferred forcerelated signal and the inferred acceleration related signal aretransformed to the time domain generating an inferred time-series offorce at the second location and an inferred time-series of accelerationat the second location.

[0013] Examples of the more important features of the invention thushave been summarized rather broadly in order that the detaileddescription thereof that follows may be better understood, and in orderthat the contributions to the art may be appreciated. There are, ofcourse, additional features of the invention that will be describedhereinafter and which will form the subject of the claims appendedhereto.

BRIEF DESCRIPTION OF THE DRAWINGS

[0014] For detailed understanding of the present invention, referencesshould be made to the following detailed description of the preferredembodiment, taken in conjunction with the accompanying drawings, inwhich like elements have been given like numerals, wherein:

[0015]FIG. 1 is a schematic of a drilling system for use with a methodaccording to one embodiment of the present invention;

[0016]FIG. 2 is a block diagram of a frequency-domain method accordingto one embodiment of the present invention; and

[0017]FIG. 3 is a block diagram of a time-domain method according to oneembodiment of the present invention.

DESCRIPTION OF PREFERRED EMBODIMENTS

[0018] Referring now to FIG. 1, a conventional drilling rig 2 is shownpowering drill string 4, which conventionally consists of multiplesections of drill pipe 6 and a bottomhole assembly 11. Sections 6 areconnected to one another by tool joints 8 in the conventional manner.Drill bit 10 is connected at the bottom end of drill string 4, and canbe a rotary bit, jet or spud bit, or other type of drill bitconventional in the art. As shown in FIG. 1 drill bit 10 is connected tobottomhole assembly 11, which in turn is connected to sections 6 ofdrill string 4. The bottomhole assembly 11 is typically made up ofmultiple sections (not shown) of drill collars having a substantiallylarger diameter than that of the drill pipe 6. Provision of such abottomhole assembly 11 is conventional in the drilling art, and isuseful for housing such equipment as detectors for sensing parameters ofinterest of the drilling operation and the surrounding formation, aswell as for other conventional functions. While such a bottomholeassembly 11 is shown in FIG. 1, it should be noted that the presence ofbottomhole assembly 11 is not required for purposes of the instantinvention, such presence depending upon the particular drillingoperation being performed. However, for purposes of acoustic telemetryas will be described hereinbelow, an acoustic transmitter 13 forvibrating drill string 4, according to information to be transmittedfrom downhole to the surface, is preferably located in such a bottomholeassembly 11. Alternatively, the acoustic transmitter 13 may be locatedat other locations in the drill string 4.

[0019] In one preferred embodiment, the acoustic transmitter 13 excitesaxial vibration modes. Alternatively, the acoustic transmitter mayexcite torsional vibration modes and a combination of torsional andaxial vibration modes. Such transmitter devices are known in the art andwill not be described here further.

[0020] Detector sub 12 is connected within drill string 4 near thesurface of the earth. Sub 12 contains detectors, such as forcetransducers, accelerometers, strain gages, piezoelectric transducers,optical transducers, and the like, for detecting stress and motionrelated to vibrations in drill string 4 and generating electricalsignals corresponding to the detected vibration-induced parameters. Theelectrical signals generated from the detectors within sub 12 arecommunicated to computer system 19. Computer system 19 analyzes thesignals corresponding to the vibrations of drill string 4 to remove aportion of the unwanted noise signals to enable enhanced decoding of thedownhole transmitted information relating to the downhole measured data,according to one preferred embodiment of the invention describedhereinbelow.

[0021] The drill bit 10 generates vibrational noise as the bit 10disintegrates the formation. This noise propagates up the drill string 4and mixes with the vibrationally encoded data signal generated bytransmitter 13. In addition, drilling rig noise is generated andtransferred to the drill string 4 at the surface. Both the surfacegenerated noise and the downhole generated noise are received along withthe data signal at sub 12. The method described below is useful inremoving a portion of the surface generated noise for enhancingdetection of the data signal transmitted downhole. Other techniquesknown in the art may be used for minimizing the downhole generatednoise.

[0022] The present invention uses vibration-state inference to estimatethe vibration state at one location in the drill string from vibrationmeasurements made at another location in the same drill string. Theobjective is to remove the influence of unwanted vibration sources(noise) on the measurements while correcting for changes made to thesignal by the transmission path (the drill string). In a typicalpreferred embodiment, the measurement location is at the surface and theinference position is at the downhole transmitter. Alternatively, inanother preferred embodiment, for transmission of command signals to adownhole tool, the surface may be the inferred position and themeasurements may be made at a downhole location.

[0023] Vibration-state inference requires determining both stress(either axial or torsional), and motion in the drill string 4. Thedetermination of stress (axial and torsional) is commonly accomplishedby determining a related strain with strain gages (not shown) or forcemeasuring devices known in the art. For purposes of the followingdiscussion and theoretical analysis, strain and stress are to beconsidered interchangeable indications for stress in the drill string 4.The motion measurement typically detects displacement, velocity, oracceleration of the drill string 4. Both axial and torsional (orrotational) motions may be detected. One skilled in the art willrecognize that accelerometer and velocity measurements can be related todisplacement using common techniques. For purposes of the followingdiscussion and theoretical analysis, acceleration, displacement, andvelocity are to be considered interchangeable indications for motion ofthe drill string 4.

[0024] Vibration-state inference relies on the knowledge of themechanical system between the position of measurement and the positionof inference, called the transmission interval, and the assumption thatthere is no externally applied excitation within the transmissioninterval. Of major utility is that the vibration-state inferencetechnique does not depend on knowledge outside the transmissioninterval. Therefore, knowledge (or measurement) of the top and bottomboundary conditions (noise of the drill bit and surface equipment) ofthe drill string are not needed.

[0025] Theory:

[0026] The equation of motion for longitudinal vibrations of a uniformdrill string is $\begin{matrix}{{{\rho \quad A\quad \frac{\partial^{2}{u\left( {x,t} \right)}}{\partial t^{2}}} + {\mu \quad \frac{\partial{u\left( {x,t} \right)}}{\partial t}} - {E\quad A\quad \frac{\partial^{2}{u\left( {x,t} \right)}}{\partial x^{2}}}} = 0} & (1)\end{matrix}$

[0027] Therefore, $\begin{matrix}{{\frac{\partial^{2}{u\left( {x,t} \right)}}{\partial t^{2}} + {\frac{\mu}{\rho \quad A}\frac{\partial{u\left( {x,t} \right)}}{\partial t}} - {c_{0}^{2}\frac{\partial^{2}{u\left( {x,t} \right)}}{\partial x^{2}}}} = 0} & (2)\end{matrix}$

[0028] Where $\begin{matrix}{c_{0}^{2} = \frac{E}{\rho}} & (3)\end{matrix}$

[0029] In the above equations, function u(x,t) represents thedisplacement, A the cross sectional area, ρ the mass density of thematerial of the drill string, μ the damping coefficient, c₀ the velocityof longitudinal waves and E is the Young's modulus.

[0030] Consider solutions of the form

u(x,t)=u ₀(x)e ^(jωt)  (4)

[0031] On substituting equation 4 in equation 3${{\left\lbrack {{- \omega^{2}} + {j\quad \frac{\mu \quad \omega}{\rho \quad A}}} \right\rbrack u_{0}} - {c_{0}^{2}\frac{^{2}u_{0}}{x^{2}}}} = 0$

$\begin{matrix}{{\frac{^{2}u_{0}}{x^{2}} + {\frac{\omega^{2}}{c_{0}^{2}}\left( {1 - {j\quad \frac{\mu}{\rho \quad A\quad \omega}}} \right)u_{0}}} = 0} & (5)\end{matrix}$

[0032] The unknown complex function u₀(x) therefore satisfies theequation of the form $\begin{matrix}{{\frac{^{2}u_{0}}{x^{2}} + {k^{2}u_{0}}} = 0} & (6)\end{matrix}$

[0033] where, $\begin{matrix}{k^{2} = {\frac{\omega^{2}}{c_{0}^{2}}\left( {1 - {j\quad \frac{\mu}{\rho \quad A\quad \omega}}} \right)}} & (7)\end{matrix}$

[0034] The solution of equation 6 is

u ₀ =A ₁ sin(kx)+B ₁ cos(kx)  (8)

[0035] The force f₀ is given by $\begin{matrix}{f_{0} = {E\quad A\quad \frac{\partial u_{0}}{\partial x}}} & \quad & \quad & (9) \\{\quad {= {E\quad A\quad {k\quad\left\lbrack {{A_{1}{\cos ({kx})}} - {B_{1}{\sin ({kx})}}} \right\rbrack}}}\quad} & \quad & \quad & (10)\end{matrix}$

[0036] Consider the following boundary conditions:

[0037] At the top (x=0), using equation 8, the displacement u_(s) is

u _(s) =u ₀|_(x=0) =B ₁  (11)

[0038] and using equation 10, the force f₀ at x=0 is

f _(s) =f ₀|_(x=0) =E Ak A ₁  (12)

[0039] Similarly, at a downhole location l feet away (x=l), thedisplacement u_(d) is

u _(d) =u _(0|) _(x=l) =A ₁ sin(kl)+B ₁ cos(kl)  (13)

[0040] and the force f_(d) at x=l is

f _(d) =f ₀|_(x=l) =E Ak[A ₁ cos(kl)−B ₁ sin(kl)]  (14)

[0041] The four equations 11-14 can be used to obtain the displacementand force (u_(d) & f_(d)) at downhole location in terms of the measureddisplacement and force (u_(s) & f_(s)) at the surface location asfollows:

[0042] Substitute A₁ & B₁ from equations 11 & 12 into equation 13$\begin{matrix}{u_{d} = {{\frac{1}{E\quad A\quad k}{\sin ({kl})}f_{s}} + {{\cos ({kl})}u_{s}}}} & (15)\end{matrix}$

 f _(d)=cos(kl)f _(s) −E Ak sin(kl)u _(s)  (16)

[0043] From equation 4 it can be easily seen that the velocity (v) andacceleration (a) are given by $\begin{matrix}\begin{matrix}{v = {\frac{u}{t} = {j\quad \omega \quad {u_{0}(x)}^{j\quad \omega \quad t}}}} \\{a = {\frac{^{2}u}{t^{2}} = {{- \omega^{2}}{u_{0}(x)}\quad ^{j\quad \omega \quad t}}}}\end{matrix} & (17)\end{matrix}$

[0044] Equation 15 and 16 can therefore, be expressed in terms ofvelocity v_(d) & v_(s) as $\begin{matrix}{v_{d} = {{\frac{j\quad \omega}{E\quad A\quad k}{\sin ({kl})}f_{s}} + {{\cos ({kl})}v_{s}}}} & (18)\end{matrix}$

$\begin{matrix}{f_{d} = {{{\cos ({kl})}f_{s}} - {\frac{E\quad A\quad k}{j\quad \omega}{\sin ({kl})}v_{s}}}} & (19)\end{matrix}$

[0045] and, in terms of acceleration a_(d) & a_(s) as $\begin{matrix}{a_{d} = {{\frac{- \omega^{2}}{E\quad A\quad k}{\sin ({kl})}\quad f_{s}} + {{\cos ({kl})}\quad a_{s}}}} & (20) \\{f_{d} = {{{\cos ({kl})}f_{s}} + {\frac{E\quad A\quad k}{\omega^{2}}{\sin ({kl})}a_{s}}}} & (21)\end{matrix}$

[0046] The above equations can be expressed in the matrix form asfollows $\begin{matrix}{\begin{bmatrix}u_{d} \\f_{d}\end{bmatrix} = {\begin{bmatrix}{\cos ({kl})} & \frac{\sin ({kl})}{E\quad A\quad k} \\{{- E}\quad A\quad k\quad {\sin ({kl})}} & {\cos ({kl})}\end{bmatrix}\begin{bmatrix}u_{s} \\f_{s}\end{bmatrix}}} & (22) \\{\begin{bmatrix}v_{d} \\f_{d}\end{bmatrix} = {\begin{bmatrix}{\cos ({kl})} & {\frac{j\quad \omega}{E\quad A\quad k}{\sin ({kl})}} \\{{- \frac{E\quad A\quad k}{j\quad \omega}}{\sin ({kl})}} & {\cos ({kl})}\end{bmatrix}\begin{bmatrix}v_{s} \\f_{s}\end{bmatrix}}} & (23) \\{\begin{bmatrix}a_{d} \\f_{d}\end{bmatrix} = {\begin{bmatrix}{\cos ({kl})} & {\frac{- \omega^{2}}{E\quad A\quad k}{\sin ({kl})}} \\{\frac{E\quad A\quad k}{\omega^{2}}{\sin ({kl})}} & {\cos ({kl})}\end{bmatrix}\begin{bmatrix}a_{s} \\f_{s}\end{bmatrix}}} & (24)\end{matrix}$

[0047] Equations 24 can be written in the following general form:$\begin{matrix}{\begin{bmatrix}a_{d} \\f_{d}\end{bmatrix} = {\begin{bmatrix}T_{11} & T_{12} \\T_{21} & T_{22}\end{bmatrix}\begin{bmatrix}a_{s} \\f_{s}\end{bmatrix}}} & (28)\end{matrix}$

[0048] where $\begin{matrix}{{{T_{11} = {T_{22} = {\cos ({kl})}}},\quad {T_{12} = {{- \frac{\omega^{2}}{E\quad A\quad k}}{\sin ({kl})}\quad {and}}}}\quad {T_{21} = {\frac{E\quad A\quad k}{\omega^{2}}{\sin ({kl})}}}} & \left( {28a} \right)\end{matrix}$

[0049] In equation 24, the vector $\begin{bmatrix}a_{d} \\f_{d}\end{bmatrix}\quad,$

[0050] which is a column matrix of acceleration (displacement orvelocity) and internal force, is known as the state vector. Equation 24shows that the state vector at a surface location s is transferred tothe state vector at the downhole location d at distance l, through thesquare matrix, which is known as the transfer matrix. It is a functionof the elastic and dynamic properties of the drill string system andfrequency. Therefore, for known values of the state vector at thesurface and a chosen value of frequency, ω, it is possible to infer (orcompute) the state vector at the downhole location, for known propertiesof the drill string.

[0051] As is commonly known, a typical drill string comprises drillcollars and drill pipe sections with varying lengths and diameters. Fora series of varying tubulars, each characterized by its own transfermatrix, T₁, T₂, T₃, . . . Tn, the transfer matrix representing theeffect of all the tubulars connected end-to-end is:[T_(n)]·[T_(n−1)]·[T_(n−2)]· . . . ·[T₁]. For the extreme ends of thetransmission interval, for example end a and end b with a system of nconnected tubulars; $\begin{matrix}{\begin{bmatrix}{ub} \\{Fb}\end{bmatrix} = {\begin{bmatrix}\lbrack{Tn}\rbrack & \cdots & \lbrack{T3}\rbrack & \lbrack{T2}\rbrack & \lbrack{T1}\rbrack\end{bmatrix}\begin{bmatrix}{ua} \\{Fa}\end{bmatrix}}} & (29)\end{matrix}$

[0052] Note that in matrix algebra [A][B]≠[B][A], therefore order isimportant in calculating the system transfer matrix. The calculationstarts multiplying transfer matrices from the inference end, not fromthe measurement end.

[0053] Sign convention:

[0054] Using a right handed coordinate system, with x axis coincidingwith the axis of the tubular, the face with outward normal pointing inthe positive direction of the x-axis, represents the positive face ofthe section. In this arrangement, the displacements are positive if theycoincide with the positive direction of the coordinate system and forcesare positive when acting on the positive face with vector directionpointing in the positive direction.

[0055] The results in equation 28 represent the transfer matrix for thecase where the direction is from upper (or surface) to lower end(downhole), i.e. for estimating force and displacement at the lower end(downhole) using known (measured) forces and acceleration at the surface(or upper end). In essence, the signal transmitted from a downholetransmitter can be inferred from surface force and displacementmeasurements.

[0056] Evaluation of k:

[0057] From equation 7, k can be expressed as $\begin{matrix}{k = {\frac{\omega}{c_{0}}\sqrt{\left( {1 - {\frac{\mu}{\rho \quad A\quad \omega}j}} \right)}}} & (30)\end{matrix}$

[0058] It can be shown that (for example, see Kolsky, H., Stress Wavesin Solids, Ch. 5, Dover Publications, Inc, 1963) $\begin{matrix}{\frac{\mu}{\rho \quad A} = {2\quad \alpha \quad c_{0}}} & (31)\end{matrix}$

[0059] Where α is the attenuation coefficient. Also, $\begin{matrix}{\alpha = \frac{\omega}{2\quad Q\quad c_{0}}} & (32)\end{matrix}$

[0060] On substituting equations 31 and 32 into equation 30 therefore$\begin{matrix}{k = {\frac{\omega}{c_{0}}\sqrt{\left( {1 - {\frac{1}{Q}j}} \right)}}} & (33)\end{matrix}$

[0061] where Q is a quality factor representing the sharpness of aresonance peak of the vibrational system.

[0062] The solution to Equations 22-24 and equations 28 and 29 can beeasily obtained using a computer using techniques known in the art.

[0063] The above inference-state analysis is directed to longitudinal(axial) vibrations, but is also valid for torsional vibrations by makingthe following substitutions into the above equations;

[0064] replace

[0065] E by G, the shear modulus;

[0066] u by θ, the angular displacement;

[0067] f by T, torque;

[0068] A by I_(p), the polar moment of inertia; and

[0069] c_(t) ²=G/ρ, the shear wave velocity.

[0070] Also note that the above analysis concerns steady-stateconditions or frequency domain operations only. However, steady-stateconditions are not required. Time-domain (arbitrary/non-periodic)signals may be analyzed as well if the initial (time zero) vibrationstate at the inference point is known. Many time-frequency domaintransformation algorithms, for example discrete Fourier transforms anFast-Fourier transforms implicitly assume that the time data signal, orrecord, is periodic (i.e. that it repeats itself indefinitely). Realworld signals, however, are commonly finite in length. Techniques areknown in the art to deal with data that are not truly periodic whilestill enjoying the utility of digital transform methods. One methodinvolves “windowing” the finite length record. This techniqueessentially tapers the beginning and ending segments of the record suchthat it may be considered to be periodic. Various window functions areknown in the art and include, but are not limited to, (i) Hanning, (ii)Hamming, and (iii) Blackman. The use of such techniques yield resultsfor the finite length signal record that approximate the spectralcharacteristics of a periodic signal with similar characteristics.

[0071] In a frequency domain operational example, shown in block diagramform in FIG. 2, in 201, downhole transmitter 13 imparts encoded datasignals into the drill string 4 that travel through the drill string 4toward the surface. In 202, the drill string acceleration a_(s) anddrill string force f_(s) are measured at surface receiver 12 and inputas time-series data to computer system 19 for analysis. In 203,mechanical data, such as lengths and diameters, and mechanicalproperties, such as density and elastic modulus, are input for eachdrill string section between the measuring location and the downholeinference location at transmitter 13. The mechanical data and mechanicalproperties are used to compute a transfer matrix using the techniquesdescribed herein, see 204. In 205, the acceleration and forcetime-series data are transformed to the frequency domain usingtechniques known in the art, such as the Fourier transform. In 206, thetransformed acceleration and force measurements are multiplied, in thefrequency domain, by the transfer matrix as described previously tocalculate an inferred acceleration and inferred force, in the frequencydomain, at the downhole inference location at transmitter 13. In 207,the frequency domain inferred downhole acceleration and inferreddownhole force are transformed back to the time domain using Fouriertransform, or equivalent techniques, thereby generating inferredacceleration and force time-series data that can be decoded in step 208to yield the downhole encoded and transmitted data. The sequencedescribed above relates to data sent from a downhole location to asurface location but could also be used for transmitting data from asurface location to a downhole location.

[0072] Alternatively, in a time domain operational example, shown inblock diagram form in FIG. 3, in 301, downhole transmitter 13 impartsencoded data signals into the drill string 4 that travel through thedrill string 4 toward the surface. In 302, the drill string accelerationa_(s) and drill string force f_(s) are measured at surface receiver 12and input as time-series data to computer system 19 for analysis. In303, mechanical data, such as lengths and diameters, and mechanicalproperties, such as density and elastic modulus, are input for eachdrill string section between the measuring location and the downholeinference location at transmitter 13. The mechanical data and mechanicalproperties are used to compute a transfer matrix using the techniquesdescribed herein, see 304. In 305, the frequency dependent transfermatrix is transformed to the time domain using techniques known in theart, such as the Fourier transform. One skilled in the art willappreciate that just as the time domain signal must be shaped orwindowed to provide acceptable results, so to the frequency signal mustbe shaped, for example, by band-limiting the Fourier coefficients. Thisensures that the resultant operator is sufficiently tapered toaccurately approximate a periodic signal, when transformed. In 306, theacceleration and force measurements are combined with the transfermatrix using standard convolution methods to calculate an inferredacceleration and inferred force, in the time domain, at the downholeinference location at transmitter 13, thereby generating inferredacceleration and force time-series data that can be decoded in step 207to yield the downhole encoded and transmitted data. The sequencedescribed above relates to data sent from a downhole location to asurface location but could also be used for transmitting data from asurface location to a downhole location.

[0073] A major advantage in using the transfer matrix method is that alarge, complex system can be broken down into its components which havesimple elastic and dynamic properties. Calculations can be then made, byproceeding from one component to the other, starting from one end of thefirst component to the next and so on. In a drill string, the componentscan be drill pipes, drill collars, etc. with different dimensions andmaterial properties. This technique is computationally more efficientthan solving such a system using other common techniques such as finiteelement methods.

[0074] In the method discussed above, it has been shown (using equation24) that it is possible to infer or estimate the motion (i.e.displacement, velocity or acceleration) and force (or stress) at onelocation from known (measured) motion and stress at another locationthereby enabling improved acoustic drill string telemetry. The knowledgeof boundary conditions or noise sources outside the interval between themeasurement point and the inference point is not needed.

[0075] The foregoing description is directed to particular embodimentsof the present invention for the purpose of illustration andexplanation. It will be apparent, however, to one skilled in the artthat many modifications and changes to the embodiment set forth aboveare possible without departing from the scope and the spirit of theinvention. It is intended that the following claims be interpreted toembrace all such modifications and changes.

What is claimed is:
 1. A method of acoustic telemetry in a drill stringin a wellbore, comprising: a. transmitting an acoustic signal related toa parameter of interest from a transmitting location into the drillstring; b. detecting signals propagated through the drill string at areceiving location, said detected signals including noise; c.determining a drill string transfer matrix defining the propagation ofsignals through a transfer interval between the receiving location andthe transmitting location; and d. using said detected signals and thedrill string transfer matrix for obtaining an estimate of the acousticsignal.
 2. The method of claim 1 wherein detecting signals at areceiving location comprises detecting a first time-series ofmeasurements related to a force on said drill string and a secondtime-series of measurements related to a motion of said drill string. 3.The method of claim 2 wherein using said detected signals and the drillstring transfer matrix for obtaining an estimate of the acoustic signalcomprises: a. transforming said first time-series of measurements andsaid second time-series of measurements to a frequency domain; b.combining said transformed first time-series of measurements and saidtransformed second time-series measurements with said transfer matrix togenerate an inferred force related signal at said second location and aninferred motion related signal at said second location; c. transformingsaid inferred force related signal and said inferred motion relatedsignal to the time domain generating an inferred time-series force atsaid second location and an inferred time-series motion at said secondlocation; and d. decoding said inferred force signal and said inferredmotion signal to determine said transmitted parameter of interest. 4.The method of claim 1 wherein determining the drill string transfermatrix comprises: i. inputting data related to mechanical properties andmaterial properties for each of a plurality of sections of the drillstring; ii. calculating for each of the plurality of sections of thedrill string, a transfer matrix related to each section of the drillstring; and iii. combining each of the plurality of section transfermatrices with each succeeding section transfer matrix.
 5. The method ofclaim 1 wherein the transmitting location is a downhole locationproximate a bottom end of the drill string and said receiving locationis proximate a top end of the drill string.
 6. The method of claim 1wherein the transmitting location is proximate a top end of the drillstring and the receiving location is downhole proximate a bottom end ofthe drill string.
 7. The method of claim 2, wherein the measurementrelated to drill string motion is one of (i) an acceleration, (ii) avelocity, and (iii) a displacement.
 8. The method of claim 2 whereinusing said detected signals and the drill string transfer matrix forobtaining an estimate of the acoustic signal comprises: i. transformingsaid transfer matrix to a time domain; ii. combining said firsttime-series of measurements and said second time-series of measurementswith said transformed transfer matrix to generate an inferred forcerelated signal at said second location and an inferred motion relatedsignal at said second location; and iii. decoding said inferred forcesignal and said inferred motion signal to determine said transmittedparameter of interest.
 9. The method of claim 3, wherein the step oftransforming said first time-series of measurements and said secondtime-series of measurements includes windowing said first time-series ofmeasurements and said second time-series of measurements.
 10. The methodof claim 3, wherein the step of transforming said inferred force relatedsignal and said inferred motion related signal to the time domainincludes band-limiting said inferred force related signal and saidinferred motion related signal in the frequency domain beforetransformation to the time domain.
 11. A method of reducing noise in anacoustic signal transmitted at a second location and received at a firstlocation in a drill string, comprising: a. calculating a transfer matrixrelated to a transmission interval of the drill string; b. detectingtime series data sets of vibrations at said first location comprising afirst time-series data set of measurements related to a force on saiddrill string and a second time-series data set of measurements relatedto an acceleration of said drill string; c. transforming said firsttime-series data set and said second time-series data set to a frequencydomain; d. combining said transformed first time-series data set andsaid transformed second time-series data set with said transfer functionto generate an inferred force related signal at said second location andan inferred acceleration related signal at said second location; and e.transforming said inferred force related signal and said inferredacceleration related signal to the time domain generating an inferredtime-series of force at said second location and an inferred time-seriesof acceleration at said second location.
 12. The method of claim 11wherein calculating the drill string transfer matrix comprises: i.calculating for each of a plurality of drill string sections, a transfermatrix related to each section of the drill string; and ii. combiningeach of the plurality of section transfer matrices with each succeedingsection transfer matrix.
 13. The method of claim 11 wherein the secondtransmitting location is a downhole location proximate a bottom end ofthe drill string and said first receiving location is proximate a topend of the drill string.
 14. The method of claim 11 wherein the secondtransmitting location is proximate a top end of the drill string and thefirst receiving location is downhole proximate a bottom end of the drillstring.